How do I extrude only a small portion of a face?
Let's assume you want the extrude a small portion of the plan(a).
plan(a) is 1m*1m . We will extrude 0.5m*0.5m know as plan(b):

Select plan(a),
(1)use the extrude fonction but do not extrude yet

(2)change to scale fonction and now you can extrude. You have now the plan(b) inside the plan(a). With both plan perfectily aligned.

(3)Now you can extrude plan(b)

In the picture attached the you can see the face and profile view so it will be more clear.